Magnetars are neutron stars with X-ray and soft γ-ray outbursts thought to be powered by intense internal magnetic fields. Like conventional neutron stars in the form of radio pulsars, magnetars exhibit 'glitches' during which angular momentum is believed to be transferred between the solid outer crust and the superfluid component of the inner crust. The several hundred observed glitches in radio pulsars and magnetars have involved a sudden spin-up (increase in the angular velocity) of the star, presumably because the interior superfluid was rotating faster than the crust. Here we report X-ray timing observations of the magnetar 1E 2259+586 (ref. 8), which exhibited a clear 'anti-glitch'--a sudden spin-down. We show that this event, like some previous magnetar spin-up glitches, was accompanied by multiple X-ray radiative changes and a significant spin-down rate change. Such behaviour is not predicted by models of neutron star spin-down and, if of internal origin, is suggestive of differential rotation in the magnetar, supporting the need for a rethinking of glitch theory for all neutron stars.

We present new simulations of the evolution of axially symmetric magnetic fields in neutron star crusts under the influence of the Hall effect and subdominant Ohmic dissipation. In the Hall effect, differential rotation of the electron fluid generates toroidal field by winding of the poloidal field. For this reason, we focus on the influence of the initial choice of the electron angular velocity profile on the subsequent and long-term magnetic evolution. Whereas previous simulations have generally chosen angular velocities increasing outwards, corresponding to the lowest order Ohmic mode in the crust; a more realistic choice is an angular velocity decreasing outwards, corresponding to the magnetohydrodynamic equilibrium field that is likely present at the time of crust formation. We find that the evolution passes through three basic phases. The early evolution is a response to the initial conditions. During the second phase, the field consists of poloidal and toroidal components which eventually relax to an isorotation state in which the angular velocity of the electrons becomes constant along poloidal magnetic field lines, causing Hall evolution to saturate. In the third phase, the field dissipates slowly while maintaining isorotation. We discuss the implications for the long-term field structure and observable properties of isolated neutron stars.

Significance: The observed diversity of magnetars indicates that their magnetic topology is more complicated than a simple dipole. Current models of their radiative emission, based on axially symmetric simulations, require the presence of a concealed toroidal magnetic field having up to 100 times more energy than the observed dipole component, but the physical origin of such a field is unclear. Our fully 3D simulations of the crustal magnetic field demonstrate that magnetic instabilities operate under a range of plausible conditions and generate small-scale field structures that are an order of magnitude stronger than the large-scale field. The Maxwell stress and Ohmic heating from these structures can explain magnetar bursts and surface hotspots, using comparable poloidal and toroidal magnetic fields.

The classical Hall effect is found to drive the magnetic field of neutron star crusts towards an attractor state without a turbulent cascade.

We present solutions for Hall equilibria applicable to neutron star crusts. Such magnetic configurations satisfy a Grad–Shafranov-type equation, which is solved analytically and numerically. The solutions presented cover a variety of configurations, from purely poloidal fields connected to an external dipole to poloidal–toroidal fields connected to an external vacuum field, or fully confined within the star. We find that a dipole external field should be supported by a uniformly rotating electron fluid. The energy of the toroidal magnetic field is generally found to be a few per cent of the total magnetic field energy for the fields with an external component. We discuss the evolution due to Ohmic dissipation which leads to slowing down of the electron fluid. We also find that the transition from an MHD equilibrium to a state governed by Hall effect generates spontaneously an additional toroidal field in regions where the electron fraction changes.